Gallery owner Ray Hughes is known in the art world for his barbs. Photo: Louise Kennerley

Miller had been working from photographs of Mr Turnbull taken at his farm in Scone in the Hunter Region of NSW. Miller had stayed there with the Turnbull family for a previous commission.

For those commissioned works, Miller depicted the head and shoulders of Malcolm and Lucy Turnbull on separate canvases, in the style of Piero della Francesca's famous diptych The Duke and Duchess of Urbino. But instead of Francesca's Marche landscape in the background, Miller painted the land around Scone.

Political commentator Annabel Crabb wrote about them in her 2010 book Rise of the Ruddbot. She said the artistic reference was meant to show that, like the Duke of Urbino (known as the "Light of Italy"), Turnbull cultivated the arts and considered his wife the most important person in his world.

Miller works mainly from life now and consults his subject first. He won the Archibald in 1998 for his portrait of Allan Mitelman.

Miller said that, although he appreciated Hughes defending the failed work, he was surprised news of the destroyed portrait had come up more than 20 years later.

Mr Hughes' son Evan is running for Labor against Mr Turnbull in the Sydney electorate of Wentworth at the forthcoming Federal election.

This portrait of Malcolm Turnbull by Vivian Falk was a finalist in the 2007 Archibald Prize. This painting is still around.

"It's only coming up because Evan is going up against Malcolm," Miller said. "It's pretty obvious Evan is trying to get attention."

Evan Hughes said his father was known in the art world for his barbs and he stood by Miller's merits as an artist.

"Dad's got a reputation for being sardonic and I'm sure that the Prime Minister has a sense of humour about that."

Mr Hughes said he respected Mr Turnbull and did not think the Prime Minister "possesses any of the qualities that the anecdote mentions".

Mr Turnbull is not the only politician to have disliked an artist's work.

On his 80th birthday in 1954, British prime minister Winston Churchill was presented with a portrait by noted artist Graham Sutherland. The 1000 guinea fee had come from donations from his colleagues in the hope the painting would hang in Westminster after his death.

But Churchill hated the painting, describing it privately as "filthy" and "malignant". In public he was more measured, calling it "a remarkable example of modern art".

He took the portrait home where, not long afterwards, it was destroyed by his wife.